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| Whitehead A.N. — A Treatise on Universal Algebra with Applications, Vol. 1 |
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| Предметный указатель |
Absolute in connection with Congruent Transformations 456 sqq 500
Absolute in connection with Conic Section, defined 497;
Absolute in connection with Plane 367 496
Absolute in connection with Point-pair, defined 351;
Absolute in connection with Points on, in Hyperbolic Geometry 422;
Absolute in connection with Polar Begions 367 384 420;
Absolute in connection with Quadric, defined 355
Absorption, Law of 36 sqq.
Acceleration in Euclidean Space 540 xqq.;
Acceleration in Non-Euclidean Space 482 sqq
Addition and Multiplication 25 sqq.
Addition and Positional Manifolds 120 sqq.
Addition in Algebra of Symbolic Logic 35 sqq.
Addition in connection with Classification of Algebras 29 sqq.;
Addition of vectors 507 sqq.
Addition, Principles of, in Universal Algebra, defined 19 sqq.
Addition, Relations 123
Algebra, Linear, and Algebra of Symbolic Logic 35
Algebra, Linear, defined 28
Algebra, Linear, mentioned 32 172;
Algebra, Universal, defined 18.
Algebra, Universal, mentioned 11 35
Algebras, classification of 29 sqq.
Algebras, Linear Associative 30
Algebras, Numerical Genus of 29 119
Algebras, Species of, defined 27
Angle of Contingence and 552;
Angle of Contingence, in Euclidean Space 539
Angle of Contingence, in Non-Euclidean Space 479;
Angle of Parallelism, in Hyperbolic Space 438
Angle of Torsion, in Euclidean Space 540;
Angle of Torsion, in Non-Euclidean Space 479
Angular Distance between Points in Anti-space 417
Anharmonic Ratio in Positional Manifolds, defined 132;
Anharmonic Ratio of Systems of Forces 290.
Anti-space, considered 414 sqq.;
Anti-space, defined 354
Anti-spatial Elements 414 sqq.
Antipodal Elements, defined 166;
Antipodal Elements, in Elliptic Space 361
Antipodal Form of Elliptic Geometry, defined 355;
Antipodal Intercept, defined 168;
Antipodal Intercept, length of 362
Arbitrary Regions in Algebra of Symbolic Logic 55 sqq.
Arithmetic and Algebra 11
Associated Quadric of Triple Group see Group; System of Forces see
Associative Law and Algebra of Symbolic Logic 37;
Associative Law and Combinatorial Multiplication 174
Associative Law and Matrices 251;
Associative Law and Multiplication 27;
Associative Law and Pure and Mixed Products 185;
Associative Law and Steps 25;
Associative Law, defined 21
Ausdehnungslehre 13 19 32 115 131 168 171 172 180 198 210 219 229 248 262 278 317 522 573.
Axis of a Congruent Transformation in Elliptic Space 471;
Axis of a Congruent Transformation in Euclidean Space 501
Axis of a Congruent Transformation in Hyperbolic Space 458
Axis of a Dual Group see Group.
Axis, Central, in Elliptic Geometry 401;
Axis, Central, in Euclidean Geometry 529
Axis, Central, in Hyperbolic Geometry 454
Ball, Sir B.S. 281 370 406 462 473 475 531 532
Base point 518
Beltrami 369 451
Binomial Expressions in Symbolic Logic 45 sqq.
Biquaternions 370 398.
Bolyai, J. 369 426 436 451 487;
Bolyai, J., Wolfgang 369.
Boole 4 10 35 46 63 96 111 115 116
Bradley 6 10
Brianchon's theorem 231
Buchheim 248 253 254 278 370 405 575.
Burali — Forti 522 575
Burnside 370.
Calculus, General Nature of, denned and discussed 4 sqq.;
Calculus, General Nature of, of Extension, Algebraic Species of 28 31
Calculus, General Nature of, of Extension, and Descriptive Geometry 132 214
Calculus, General Nature of, of Extension, and Theory of Duality 146 196 212 481;
Calculus, General Nature of, of Extension, investigated 169 sqq.
Cantor, G. 16.
Carried Functions 569 sqq.
Cayley 119 131 135 161 248 249 351 352 353 354 369
Central Axis see Axis.
Central Plane of Sphere in Hyperbolic Geometry 442.
Centre of Dual Group see Group.
Characteristic Lines of Congruent Transformation 470
Characteristics of a Manifold 13
Characteristics of a Scheme 9 14;
Chasles 246.
Circle, defined, and Perimeter of, in Elliptic Geometry 375;
Circle, Great, on Sphere in Hyperbolic Geometry 448
Circle, on Sphere in Hyperbolic Geometry 484.
Classification (operation in Symbolic Logic) 41
Clebsch 369 569 570;
Clebsch and Lindemann 278 280 294
Clifford 13 369 370 398 406t 409 472
Co-ordinate Elements, defined 125;
Co-ordinate Region, defined 126
Co-ordinates, Conjugate, denned 148.
Co-ordinates, Curvilinear, in Euclidean Space 543;
Co-ordinates, Curvilinear, in Non-Euclidean Space 488 494;
Combination, General Definition of 8
Common Null Line of a Group 286
Commutative Law and Algebra of Symbolic Logic 37;
Commutative Law and Congruent Transformations 464;
Commutative Law and Multiplication 27
Commutative Law, defined 21.
Complete Manifold, defined 15
Complex Intensity 120.
Complexes, Conjunctive and Disjunctive, defined and discussed 107 sqq.;
Complexes, Linear 278 sqq.
Compound Extensive Magnitudes, denned 177 sqq.
Congruence of Terms, defined 122
Congruences of Lines and Dual Groups 288
Congruent Ranges, defined 350;
Congruent Ranges, Klein's Theorem concerning 353
Congruent Transformations and Work 469 477 537
Congruent Transformations in Euclidean Geometry 500 sqq. 53Qsqq.;
Congruent Transformations in Non-Euclidean Geometry 456 sqq.;
Congruent Transformations, Associated Systems of Forces of 466 476 536
Congruent Transformations, Parameters of 460 471
Conies, Descriptive Geometry of 229 sqq
Conjugate Co-ordinates, defined and discussed 148sqq.
Conjugate lines 277;
Conjugate Sets of Systems of Forces 298 306 308.
Conjunctive Complex 107 sqq
Construction in a Positional Manifold, defined 214;
Construction, Grassmann's 219 sqq.;
Construction, Linear, of Cubics 233 sqq.;
Construction, von Staudt's 215 sqq
Content, Theory of 370 406 462
Contingence, Angle of see Angle.
Cox, Homersham 346 370 399 400 401 575
Cubics, Linear Construction of 233 sqq.
Curl, defined 554;
Curl, Flux, defined 554;
Curl, Lines and Filaments, defined 567
Curvature of Curves and Surfaces in Euclidean Space 544 sqq
Curvature of Curves and Surfaces in Non-Euclidean Space 479 sqq
Curve-Locus in Space of v Dimensions, defined 130;
Curve-Locus, Quadriquadric 144 151.
Curvilinear Locus in Space of » Dimensions, defined 130
Cylindroid in Euclidean Space 532;
Cylindroid in Non-Euclidean Soace 403
De Morgan 32 100 122 131
Dependence in a Positional Manifold, defined 123.
Derivation, General Definition of 8.
Determinants and Combinatorial Multiplication 180;
Determinants, associated with Matrices 252.
Determining Property of a Scheme 8.
| Developable Surface in Non-Euclidean Geometry 481.
Development in the Algebra of Symbolic Logic 45 sqq.
Diametral Plane of a Dual Group in Euclidean Space 532.
Differential, distinguished from Universal Algebra 18 sqq.
Dimensions of a Manifold, denned 17
Direct Transformation of a Quadric 338 sqq.;
Direct Transformation of the Absolute 456 sqq
Director Force, Line, or Equation, of a Group 286 sqq.
Discourse, Universe of 100
Discriminants of Equations, defined and discussed 51 sqq.;
Discriminants of Sub sumptions, denned 59
Disjunctive Complex 107 sqq
Displacements of Bigid Bodies in Euclidean Space 500 sqq. 536;
Displacements of Bigid Bodies in Non-Euclidean Space 456 sqq.;
Displacements Vector 472 sqq
Displacements, Small 464 476;
Displacements, Surfaces of Equal 462 472;
Distance in Elliptic Geometry, Shortest 385 387
Distance in Hyperbolic Geometry 416 sqq.;
Distance in Hyperbolic Geometry between Planes 428
Distance in Hyperbolic Geometry, Angular between Points 417
Distance in Hyperbolic Geometry, Shortest 429 sqq.;
Distance in Non-Euclidean Geometry between Sub-regions 365 sqq.;
Distance in Non-Euclidean Geometry between Sub-regions, Definition of 352
Distance, General Theory of 349 sqq.;
Distributive Law in Algebra of Symbolic Logic 37 84 174.
Divergence, defined 554
Division in Algebra of Space in Non-Euclidean Geometry 355 379.
Division in Algebra of Symbolic Logic 80 sqq.
Dual group see Group.
Duality, Theory of 147 196 481
Dupin's Theorem in Euclidean Space 546;
Dupin's Theorem in Non-Euclidean Space 494.
Elements and Terms 21
Elements and Terms, Antipodal 166 361
Elements and Terms, Co-ordinate 125
Elements and Terms, Intensively Imaginary 166;
Elements and Terms, Intensively Imaginary, Real 166
Elements and Terms, Linear, defined 177;
Elements, Linear, in Euclidean Space 508 sqq.;
Elements, Linear, in Non-Euclidean Space 399 sqq. 452
Elements, Linear, in Positional Manifold, and Mechanical Forces 273
Elements, Null, in Symbolic Logic 35 37 38;
Elements, of a Manifold, defined 13;
Elements, of a Manifold, Secondary Properties of 14
Elements, Planar, denned 177
Elements, Regional, defined 177
Elements, Self-Normal 204 sqq.
Elements, Spatial and Antispatial, in Hyperbolic Space 414 sqq.
Elements, Supplementary, in Symbolic Logic 36 sqq
Elimination and Syllogisms 103 sqq.;
Elimination and Syllogisms from Existential Expressions 89 sqq.
Elimination and Syllogisms in Symbolic Logic, defined and discussed 47 sqq.;
Elimination and Syllogisms in Symbolic Logic, Formula for 55.
Elliptic Definition of Distance 352
Elliptic Space, Formulae for 356 sqq.
Elliptic Space, Kinematics of 470 sqq.
Elliptic Space, Parallel Lines in 404 407
Elliptic Space, Parallel Lines in Subregions in 397 sqq.
Elliptic Space, Vector Systemsof Forces in 406 sqq.
Elliptic Space, Vector Systemsof Forces in, Transformations in 472 sqq.
Elliptic Spatial Manifold, defined 355
Engel, F. 317 369 370 573
Equal Displacement, Surface of 462 472
Equations in Algebra of Symbolic Logic, viz. and Universal Propositions 105;
Equations in Extensive and Positional Manifolds viz.
Equations of Condition, defined 172
Equations of Subregions 195
Equations with many Unknowns 52
Equations with many Unknowns, Discriminants of 53
Equations with many Unknowns, Resultants of 53;
Equations, Auxiliary 71 78;
Equations, Defining, denned 162
Equations, Director, of Groups 286
Equations, Identical of Matrices 256 261;
Equations, Limiting and Unlimiting, defined 59;
Equations, Negative and Positive Constituents of, defined 50
Equations, Plane and Point 147
Equations, Reciprocal, defined 147
Equations, simultaneous 51 sqq.;
Equations, Simultaneous, Discriminants of, defined 52;
Equations, Simultaneous, Resultant of, denned 52
Equations, with many Unknowns, Johnson's Method 73 sqq.
Equations, with many Unknowns, Skew-Symmetrical 71 sqq.
Equations, with many Unknowns, Solution 65 sqq.
Equations, with many Unknowns, Symmetrical 67 sqq. 73 75
Equations, with one Unknown 49 sqq.;
Equations, with one Unknown, Discriminants of 51
Equations, with one Unknown, Resultant of 51
Equations, with one Unknown, Solution of 55
Equations, with one Unknown, Standard Form of 49
Equivalence, defined 5;
Equivalence, Definition concerning, in Universal Algebra 18;
Equivalence, in Symbolic Logic, for Propositions 108
Equivalence, in Symbolic Logic, interpreted 38
Equivalence, in Symbolic Logic, Proof of 36.
Euler's Theorem, in Euclidean Geometry 547;
Euler's Theorem, in Non-Euclidean Geometry 492.
Existential Expressions 83 sqq.
Existential Expressions and Propositional Interpretation 111 sqq.;
Existential Expressions, Resultant of, denned 90
Existential Expressions, Solution of 91.
Expressions, Field of, defined 60
Extension of Field, maximum and minimum, defined 61.
Extension, Calculus of, investigated 169 sqq.;
Extension, Calculus of, mentioned 28 31 132 146
Extensive Magnitudes, defined 176 sqq.;
Extensive Manifolds and Non-Euclidean Geometry 399 sqq. 452
Extensive Manifolds and Non-Euclidean Geometry of three dimensions 273 sqq.
Extensive Manifolds and Non-Euclidean Geometry, defined 177;
Extraordinaries, defined 119*
Field of an Expression, defined 60;
Field of an Unknown, defined 60
Field, Limited, defined 61;
Flow of a Vector, defined 572.
Flux, defined for Point and Vector Formulas 527;
Flux, defined for Pure Vector Formulae 549;
Flux, Multiplication 528 sqq.;
Flux, Operation of Taking the 522 527
Flye, Ste Marie 369
Force, defined 177;
Force, defined, Compared with Mechanical Force 273;
Force, defined, Single, Condition for 277
Forces, Director, of a Group 286;
Forces, Groups of Systems of see Groups;
Forces, Intensity of, in Euclidean Space 525
Forces, Intensity of, in Non-Euclidean Space 399 452;
Forces, Investigated 273 sqq.;
Forces, Spatial, investigated 452 sqq.;
Forces, Systems of see Systems.
Forsyth 17 573
Franklin, Mrs 98 116
Frischauf 369
Functions, Theory of 11
Gauss 488 490 543.
Generating Begions of Quadrics 147 sqq. 152
Generating Begions of Quadrics in Non-Euclidean Geometry 397 451.
Generators, Positive and Negative Systems of 207
Geometry and Algebra 11;
Geometry and Extensive Manifolds 273
Geometry of a Sphere, Euclidean 365
Geometry, Descriptive, and Calculus of Extension 214;
Geometry, Descriptive, and Calculus of many Dimensions 131
Geometry, Elliptic, Polar and Antipodal Forms, defined 355;
Geometry, Hyperbolic, Investigated 414 sqq.
Geometry, Line- 278;
Geometry, Non-Euclidean, and Cayley's Theory of Distance 351
Geometry, Non-Euclidean, and Lindemann's Theory of Forces 281;
Geometry, Non-Euclidean, Historical Note upon 369 sqq.
Geometry, Parabolic 496 sqq.
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